# Examples for 8th grade - page 3

- Axial section

Axial section of the cone is equilateral triangle with area 300 m^{2.}Calculate volume of the cone. - Hands

The clock shows 12 hours. After how many minutes will agle between hour and minute hand 80°? Consider the continuous movement of both hands hours. - River

Calculate how many promiles river Hudson average falls, if on section long 921 km flowing water from 1224 m AMSL to 154 m AMSL. - Circle chord

What is the length d of the chord circle of diameter 58 mm, if distance from the center circle is 24 mm? - Clock

How many times a day hands on a clock overlap? - Server

Calculate how many average minutes a year is the web server is unavailable, the availability is 99.99%. - Pool

The swimming pool is 4 m wide and 20 m long and 156 cm deep. How many hectoliters of water is in it, if the water is 9 cm below its upper edge. - Cuboid

The cuboid has a surface area 3380 cm^{2,}the length of its edges are in the ratio 4:3:1. Calculate the volume of the cuboid. - Bus vs. train

Bus started from point A 25 minutes before the train started from the same place. The bus went an average speed of 41 km/h, train 67 km/h. To point B train and bus arrived simultaneously. Calculate time of train journey, if train and bus travelled the. - Tetrahedral pyramid

What is the surface of a regular tetrahedral (four-sided) pyramid if the base edge a=23 and height v=8? - Triangle SAS

Calculate area and perimeter of the triangle, if the two sides are 19 cm and 80 cm long and angle them clamped is 90°. - Z9-I-4

Kate thought a five-digit integer. She wrote the sum of this number and its half at the first line to the workbook. On the second line wrote a total of this number and its one fifth. On the third row she wrote a sum of this number and its one nines. Fi - Is right?

Is triangle with sides 24, 51 and 45 right triangle? - Rectangle

The rectangle is 28 cm long and 21 cm wide. Determine the radius of the circle circumscribing rectangle. - Square

Points A[1,5] and B[-4,-5] are adjacent vertices of the square ABCD. Calculate area of the square ABCD. - Movement

From the crossing of two perpendicular roads started two cyclists (each at different road). One runs at average speed 18 km/h, the second at average speed 24 km/h. Determine the distance between them after 30 minutes cycling. - Cube diagonal

Determine length of the cube diagonal with edge 55 dm. - River

From the observatory 18 m high and 26 m from the river bank, river width appears in the visual angle φ = 14°30'. Calculate width of the river. - Scale

Swimming pool is long 110 m and 30 m wide. The plan of the city is shown as a rectangle with area 13200 cm^{2.}What scale is the city plan? - Discount

Ladies sweater was twice discounted. First by 17%, then by 17% of the new price. Its final price was 72 USD. Determine the original price of sweater.

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